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Persistent Strange attractors in 3D Polymatrix Replicators

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  • Telmo Peixe
  • Alexandre A. Rodrigues

Abstract

We introduce a one-parameter family of polymatrix replicators defined in a three-dimensional cube and study its bifurcations. For a given interval of parameters, this family exhibits suspended horseshoes and persistent strange attractors. The proof relies on the existence of a homoclinic cycle to the interior equilibrium. We also describe the phenomenological steps responsible for the transition from regular to chaotic dynamics in our system (route to chaos).

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  • Telmo Peixe & Alexandre A. Rodrigues, 2021. "Persistent Strange attractors in 3D Polymatrix Replicators," Papers 2103.11242, arXiv.org, revised Jan 2022.
    • Handle: RePEc:arx:papers:2103.11242
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    References listed on IDEAS

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    1. Hassan Najafi Alishah & Pedro Duarte & Telmo Peixe, 2019. "Asymptotic Poincaré Maps along the Edges of Polytopes," Working Papers REM 2019/70, ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.
    2. Telmo Peixe, 2019. "Permanence in Polymatrix Replicators," Working Papers REM 2019/69, ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.
    3. Gaunersdorfer Andrea & Hofbauer Josef, 1995. "Fictitious Play, Shapley Polygons, and the Replicator Equation," Games and Economic Behavior, Elsevier, vol. 11(2), pages 279-303, November.
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